Several equal spherical planets are in outer space. On the surface of each planet is a set of points which is invisible from any of the remaining planets. Prove that the sum of the areas of all these sets equals the surface area of one planet.
Several equal spherical planets are in outer space. On the surface of each planet is a set of points which is invisible from any of the remaining planets. Prove that the sum of the areas of all these sets equals the surface area of one planet.
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